This comes up repeatedly, so you may want to do a forum search.
In a nutshell:
If you wanted to remove CS5, you should have done so before installing CS6. The CS5 uninstaller is very likely to mess with and destroy the CS6 installation.
Your best bet now is to use the CS6 uninstaller and uninstall CS6 first, then use the CS5 uninstaller to uninstall CS5, then run the Adobe CSClean script (downloadable from the Adobe site), and finally install CS6 again.
All adobe updaters are FULL installers and do not need a previously installed version to work. When they don't find a prior version installed, they will simply prompt you for the old serial number as well as the new one.